In an athletic composition, the probability that an athlete wins a 100m race is (frac{1}{8}) and the probability that he wins in high jump is (frac{1}{4}). What is the probability that he wins only one of the events?
-
A.
(frac{3}{32}) -
B.
(frac{7}{3}) -
C.
(frac{5}{3}) -
D.
(frac{5}{16})
Correct Answer: Option D
Explanation
Pr. (winning 100m race) = (frac{1}{8})
Pr. (losing 100m race) = 1 – (frac{1}{8}) = (frac{7}{8})
Pr. (winning high jump) = (frac{1}{4})
Pr. (losing high jump ) = 1 – (frac{1}{4}) = (frac{3}{4})
Pr. (winning only one) = Pr. (Winning 100m race and losing high jump) or Pr.(Losing 100m race and winning high jump)
= ((frac{1}{8} times frac{3}{4})) + ((frac{7}{8} times frac{1}{4}))
= (frac{3}{32} + frac{7}{32})
= (frac{10}{32})
= (frac{5}{16})